JP5653536B2 - LLR calculator and error correction decoding apparatus - Google Patents

Description

  The present invention relates to an LLR calculator that calculates a bit log likelihood ratio (hereinafter referred to as LLR) representing the reliability of transmission bits from symbol coordinates of received signal points received by a receiver of a communication system. And an error correction decoding apparatus using the same.

  In order to perform soft-decision decoding of an error correction code such as a Low-Density Parity-Check (LDPC) code or a turbo code, as shown in FIG. 1, transmission is performed from symbol coordinates of received signal points received by the receiver of the communication system. The LLR representing the bit reliability is calculated by the LLR calculator 100, and the calculated bit LLR is input to the soft decision error correction decoder 110 to perform error correction decoding to calculate an estimated bit sequence.

When the modulation scheme used in the communication system is a multi-level modulation scheme such as Phase Shift Keying (PSK), Amplitude Phase Shift Keying (APSK), or Quadrature Amplitude Modulation (QAM), one transmission symbol point is composed of a plurality of bits. Of these, if the bit LLR of the k-th bit is set to L _k , L _k is calculated by equation (1).

In Expression (1), r is a position vector (I coordinate, Q coordinate) of a received signal point, s _i is a position vector of a transmission symbol point, C _{k, 0} is a set of all transmission symbol points whose k-th bit is 0 , C _{k, 1} is a set of all transmission symbol points whose k-th bit is 1, and σ is a standard deviation of Gaussian noise in the communication channel.

  In order to calculate the bit LLR using the equation (1), the exponential function exp must be calculated and the logarithmic function ln must be calculated with respect to the result of adding the exponential function exp. It is not realistic from the viewpoint of circuit scale to implement this calculation by a circuit.

On the other hand, for example, Non-Patent Document 1 shows an approximation method in which only the maximum value is left and the others are ignored among the exps added in Expression (1). This approximation method is expressed by equation (2). In the equation (2), s _{k, 0, min} is a position vector of a point closest to the reception signal point r among transmission symbol points where the kth bit is 0, and s _{k, 1, min} is k It is a vector of points closest to the reception signal point r among transmission symbol points whose 1st bit is 1.

The LLR calculation method based on Equation (2) in Non-Patent Document 1 will be described with reference to the drawings, taking 256QAM, which is one of multilevel modulation schemes, as an example. As shown in FIG. 2, 256QAM is a multi-level modulation scheme in which one symbol is composed of 8 bits a ₁ a ₂ a ₃ ... A ₈ and there are 256 transmission symbol points. In the LLR calculation method based on Expression (2), first, as shown in FIG. 3, the transmission symbol points _{sk, 0, min} and _{sk, 1, min} are calculated based on the distance from the reception signal point r. These two transmission symbol points are referred to as reference points, and a reference point is _{obtained by} combining two reference points whose k-th bit is 0 and 1, such as a set of s _{k, 0, min} and s _{k, 1, min.} I will call it a pair. Next, the square of the distance from the reception signal point r is calculated for each reference point of the reference point pair. _Then, subtracting _{s k, 1, s k} from the square of the distance between _min and _{r, 0, min} and the square of the distance between r. Then, dividing the subtraction result by 2 [sigma] ^2. This calculation is expressed by equation (2). Actually, such a calculation is performed for each k, and an approximate value of the bit LLR for each of 8 bits constituting one symbol of 256QAM is calculated. The bit LLR of the kth bit calculated by the method of Non-Patent Document 1 is hereinafter referred to as L1 _{, k} .

  Non-Patent Document 2 describes another bit LLR calculation method. In the configuration of Non-Patent Document 2, feedback is installed from the LDPC decoder 210 at the subsequent stage of the LLR calculator 200 to the LLR calculator 200 as shown in FIG. The LDPC decoder 210 performs iterative decoding of the LDPC code by the sum product decoding method, and feeds back a decoding intermediate result (estimated bit string) obtained each time it is repeated to the LLR calculator 200.

In Non-Patent Document 2, a reference point pair is determined based on a decoding intermediate result obtained with the configuration of FIG. When the reference point pair is s _{k, 0, dec} , s _{k, 1, dec} , the LLR is calculated by an equation that approximates equation (1) as equation (3). Note that s _{k, 0, dec} is a transmission symbol point in which the k-th bit is 0 and the other bits have the same value as the decoding result, and _{sk, 1, dec} is the k-th bit and the other bits are This represents a transmission symbol point having the same value as the result of decoding. An example is shown in FIG. As is clear from the comparison of Expression (3) and Expression (2), the non-patent document 1 and the non-patent document 2 have the same LLR calculation method except for the method of determining the reference point pair. The bit LLR of the k-th bit calculated by the method of Non-Patent Document 2 is hereinafter referred to as L _{2, k} .

F. Tosato and P. Bisaglia, “Simplified soft-output demapper for binary Interleaved COFDM with application to HIPERLAN / 2,” in Proc. Int. Conf. Commun., Sep. 2002, pp. 664-668. T. Wadayama, “A Coded Modulation Scheme Based on Low Density Parity Check Codes,” IEICE transactions on fundamentals, vol. E84-A, no. 10, pp. 2523-2527, Oct. 2001.

  In the conventional bit LLR calculation method, approximation is performed by designating two transmission symbol points as reference points and ignoring other transmission symbol points. The original ideal bit LLR calculation formula is an expression including all transmission symbol points in the multi-level modulation method, and the conventional approximation method in which approximation is performed by ignoring transmission symbol points other than two is approximate. There was a problem of low accuracy. As a result, there has been a problem that the decoding performance of the soft decision error correction decoder is greatly degraded.

  The present invention has been made to solve the above-described problems, and an object thereof is to obtain an LLR calculator and an error correction decoding apparatus capable of improving the approximation accuracy of the calculated LLR.

  An LLR calculator according to the present invention is an LLR calculator of a receiver that receives a signal in which an error correction coded bit string is modulated by a multi-level modulation method, and calculates an LLR (log likelihood ratio) A reference point pair determination unit that determines two reference point pairs by selecting two transmission symbol points having a target bit of 0 and one transmission symbol point of 1, and for each of the two reference point pairs An LLR calculation unit that calculates a value obtained by adding the correction term that is zero in some cases to the added value and calculating the LLR for the two reference point pairs. It is equipped with.

  The LLR calculator according to the present invention determines two reference point pairs by selecting two transmission symbol points whose bits to be LLR calculation are 0 and two transmission symbol points which are 1, and determines two reference point pairs. Two LLRs calculated for each pair are weighted and added, and a value obtained by adding a correction term that is 0 in some cases to the added value is calculated as an LLR for two pairs of reference points. As a result, the approximation accuracy of the calculated LLR can be improved.

It is a block diagram which shows the receiver of a communication system. It is explanatory drawing which shows the transmission symbol point in a multi-value modulation system. It is explanatory drawing which shows a LLR calculation method. It is a block diagram for demonstrating another conventional LLR calculation method. It is explanatory drawing which shows another conventional LLR calculation method. It is a block diagram which shows the LLR calculator by Embodiment 1 of this invention. It is a block diagram which shows the LLR calculator by Embodiment 2 of this invention. It is a block diagram which shows the error correction decoding apparatus by Embodiment 3 of this invention. It is a block diagram which shows the internal structure of the LLR calculator of the error correction decoding apparatus by Embodiment 3 of this invention. It is a block diagram which shows the internal structure of the LLR calculator of the error correction decoding apparatus by Embodiment 3 of this invention. It is a block diagram which shows the LLR calculator by Embodiment 4 of this invention. It is a block diagram which shows the LLR calculator by Embodiment 5 of this invention.

Hereinafter, in order to explain the present invention in more detail, modes for carrying out the present invention will be described with reference to the accompanying drawings.
Embodiment 1 FIG.
A transmitter of a communication system that performs communication using a multilevel modulation scheme and an error correction code modulates a transmission bit string encoded with the error correction code by a multilevel modulation scheme and transmits the modulated transmission bit string. The receiver demodulates the multi-level modulation method and decodes the error correction code to obtain an estimated bit string that estimates the transmission bit string.
The present invention relates to a receiver including the LLR calculator 100 and the soft decision error correction decoder 110 as shown in FIG.

In the first embodiment, an LLR calculator that calculates a bit LLR using two reference point pairs (four reference points) will be described.
Prior to the description of the internal configuration of the LLR calculator, derivation of an LLR calculation formula that can calculate an LLR using two reference point pairs will be described.
First, from the original LLR calculation formula (1) having no approximate deterioration, all but exponential functions exp related to two reference point pairs to be used for LLR calculation are deleted to obtain an approximation formula of Formula (4).

  In the derivation process of Equation (1) to Equation (4), the exp term to be deleted from Equation (1), that is, any two reference point pairs used for LLR calculation, and any two reference points Even if you choose a pair, the formula is similar. In each embodiment including the subsequent approximation, the method of selecting two reference point pairs used for LLR calculation is not limited. A specific method of selecting two reference point pairs will be described later as an example.

Formula (4) needs to calculate the logarithm of the addition result of the exponential function exp, and the amount of calculation is large. Therefore, the amount of calculation is reduced by the following approximate expression. Expressions (5), (6), and (7) are expressions that describe an approximation method applied to Expression (4). The left side of Expression (5) represents the exponential function variable of Expression (4) by x and y, and x and y are 0 or more. The left side of Expression (5) is transformed as shown in the lower part of the right side. However, min (x, y) represents the minimum value of x and y.

  Ln (1 + exp (− | y−x |)) appearing after transformation of Expression (5) can be Taylor-expanded around 0 as in the first line of Expression (6). In terms of the equation after Taylor expansion, when the t (≧ 0) is small, the third-order or higher-order term becomes a small value, so the third-order or higher-order term is ignored. However, since the accuracy of approximation can be degraded by simply ignoring it, a constant term is added to correct this degradation. The second line of equation (6) is a combination of ln2 originally present in the first row of equation (6) and the constant term added for approximation correction, expressed as A. Note that since the left side of Equation (6) is 0 or more regardless of the value of the variable t, max (0, At / 2) is set so that the right side is also 0 or more. max (0, At / 2) represents the maximum value of 0 and At / 2.

As an example of the value of the constant A, A = 0.9. In this case, the approximate deterioration is small. Further, a better value of A may be searched and determined by computer simulation or actual machine verification of the LLR calculator and the soft decision error correction decoder. In any case, this configuration does not limit the value of A.
Formula (7) is obtained by applying Formula (6) to Formula (5) and modifying the formula.
Applying equation (7) to equation (4) yields equation (8).

  Next, the configuration of an apparatus that calculates the LLR using Equation (8) will be described. As shown in FIG. 1, an LLR calculator 100 and a soft decision error correction decoder 110 are installed in the receiver of the communication system. The configuration of the present embodiment is a configuration for the LLR calculator 100. FIG. 6 shows the configuration. This configuration includes two sets of reference point pair determination units 101, a difference calculation unit 102 for the square of the distance between a received signal point and a reference point, an LLR calculation unit 103, and a memory 104.

  The two sets of reference point pair determination units 101 select two transmission symbol points whose bit to be LLR calculation is 0 and two transmission symbol points which are 1, and determine two sets of reference point pairs. The square difference calculation unit 102 between the received signal point and the reference point calculates a square difference of the distance between the received signal point and the reference point. The LLR calculation unit 103 calculates the LLR using an LLR calculation formula provided in advance based on the value calculated by the square difference calculation unit 102 of the distance between the received signal point and the reference point. The memory 104 stores calculation intermediate values and calculation results generated during the operation of the two sets of reference point pair determination unit 101, the square difference calculation unit 102 between the received signal point and the reference point, and the LLR calculation unit 103. To do.

Next, the operation of the LLR calculator 100 of the first embodiment will be described.
The LLR calculator 100 receives the IQ plane coordinates of the reception signal point. The two sets of reference point pair determination units 101 determine reference points s _j and s _{l in} which the k-th bit of the transmission symbol is 0, and reference points s ′ _j and s ′ _{l in} which the k-th bit of the transmission symbol is 1. . Two sets of reference points are determined for each k-th bit. The subject of the present invention is a communication system using a multi-level modulation scheme in which a transmission symbol point is composed of a plurality of bits as described above. The number of bits constituting one symbol differs depending on the modulation method. If the number of bits is n, the reference point pairs obtained by the two reference point pair determination units 101 are 2n in total. However, the reference points chosen may overlap.

The reference point determined by the two sets of reference point pair determination units 101 may be any transmission symbol point, and this configuration can be realized regardless of the determination method. For example, the transmission symbol point may be selected in view of the distance from the coordinates of the reception signal point. As an example of this case, of the transmission symbol points whose k-th bit is 0, the point closest to the reception signal point and the second closest point are s _j and _sl , and the k-th bit is 1 among the transmission symbol points There is a method of selecting s ′ _j , s ′ _l as the point closest to the reception signal point and the second closest point. In such a selection method, an important reference point pair can be selected in any case, and the bit error rate of the estimated bits can be reduced.

  In FIG. 6, the reception signal point that is the input of the LLR calculator 100 is input to the two reference point pair determination units 101, but a configuration without this input is also possible. The reference point may be determined without depending on it. For example, when a transmission symbol point with high transmission frequency is known in advance, there is a method of selecting the transmission symbol point as a reference point. In this way, when transmission symbol points that are frequently transmitted are known in advance, it is possible to select a reference point pair that is more important than selecting a transmission symbol point in view of the distance from the coordinates of the reception signal point. it can. In any case, the two sets of reference point pair determination units 101 determine two sets of reference point pairs for each bit constituting the transmission symbol point.

また、同様に、ｋビット目が１の２つの基準点ｓ’_ｊ，ｓ’_ｌと受信信号点ｒとの距離の２乗をそれぞれ求め、それらの差を算出する。これらと同時に、ｋビット目が０の基準点ｓ_ｊ，ｓ_ｌのうち受信信号点ｒに近い方の点を判定し、さらにｋビット目が１の基準点ｓ’_ｊ，ｓ’_ｌのうち受信信号点ｒに近い方の点の判定を行う。これらの判定は、受信信号点ｒとｓ_ｊ，ｓ_ｌ（もしくは、ｓ’_ｊ，ｓ’_ｌ）それぞれとの距離の２乗の差を前記の通り算出すれば、その算出結果の値の正負によって判定できるのは言うまでもない。なお、受信信号点と基準点間の距離の２乗の差算出部１０２で算出するのは距離の２乗の差の値であり、距離の２乗そのものを算出する必要は必ずしもなく、同値変形した式を用いて差を算出してもよい。Next, the operation of the square difference calculation unit 102 between the received signal point and the reference point will be described. In this calculation unit, the following two values are calculated in order to determine min and max in Equation (8). One is the difference between the squares of the distances between the two reference points s _j and s ₁ whose k-th bit is 0 and the received signal point r. A specific formula is shown in Formula (9).

Similarly, k-th bit is determined two reference points s _'j, s' of 1 _l and the square of the distance between the received signal point r, respectively, and calculates the difference therebetween. At the same time, a point closer to the reception signal point r is determined among the reference points s _j and s _l whose k-th bit is 0, and further, of the reference points s ′ _j and s ′ _l whose k-th bit is 1 The point closer to the reception signal point r is determined. These determinations can be made by calculating the difference between the squares of the distances between the received signal point r and each of s _j , s _l (or s ′ _j , s ′ _l ) as described above. Needless to say, it can be determined by. Note that the distance square difference calculation unit 102 calculates the distance square difference value between the received signal point and the reference point, and it is not always necessary to calculate the distance square itself. The difference may be calculated using the formula.

E.g., I coordinates r and r (I), the Q coordinate is expressed as r _(Q), s j, when also expressed similarly I coordinate and Q coordinate of _{s l,} Equation (9) formula (10) The equivalence deformation can be performed as described above, and the calculation may be performed using Equation (10). At this time, the terms relating to s _j and s _l in equation (10) have the same value regardless of the reception signal point r. And the amount of calculation is reduced.

  In the above description of the operations of the two reference point pair determination units 101 and the difference difference calculation unit 102 of the square of the distance between the received signal point and the reference point, the k-th bit has been described. Then, the same calculation is performed for each of n bits constituting the transmission symbol point.

Next, the operation of the LLR calculation unit 103 will be described. This calculation unit calculates the LLR based on the equation (8). First, a reference point close to r of s _j and s _l calculated by the square difference calculation unit 102 of the distance between the received signal point and the reference point and a reference close to r of s ′ _j and s ′ _l From the point, two mins of the equation (8) are determined. Each min employs a term including a transmission symbol point closer to the reception signal point r. Furthermore, the two max in the equation (8) are the squares of the distances between s _j and _sl and the received signal point r, which are calculated by the square difference calculation unit 102 between the received signal point and the reference point. Calculation is performed using the difference and the difference in square of the distance between s ′ _j and s ′ _l and the received signal point r. Note that the standard deviation σ of the Gaussian noise on the communication channel may be a value estimated using a separately installed estimation device. However, since it is difficult to estimate σ, a value determined in advance by experiments, tests, simulations, etc. is used for LLR calculation. It may be set in the unit 103 and used in the equation (8). By the above operation, min and max are calculated, and the remainder is subjected to four rule operations to calculate the LLR based on the equation (8). Although the k-th bit has been described above, the LLR calculation unit 103 performs the above calculation for each bit constituting the transmission symbol point.

  The memory 104 stores calculation intermediate values and calculation results generated during the operation of the two sets of reference point pair determination unit 101, the square difference calculation unit 102 between the received signal point and the reference point, and the LLR calculation unit 103. It is used as appropriate.

In the above description, the reference point close to r of s _j and s _l and the reference point close to r of s ′ _j and s ′ _l are assumed to be unknown. Sometimes it is. This is a case where the distance from the received signal point r is used as a reference for determining the reference point pair in the two sets of reference point pair determining units 101. As an example, the k-th bit closest to the received signal point r is In this case, the transmission symbol point of 0 is set as the reference point s _j , and the transmission symbol point closest to the reception signal point r and having the k-th 1 is determined as the reference point s ′ _j . If it is known in advance that s _j and s ′ _j are close to the reception signal point, equation (8) can be simplified as equation (11). In this case, the reception signal point and the reference point Among the operations of the difference square calculation unit 102, the calculation of the reference point close to the received signal point r can be omitted, and the two min determinations of the operation of the LLR calculation unit 103 can be omitted.

  As described above, in the first embodiment, Formula (1), which is an ideal LLR calculation formula, can be approximated by an approximation formula using two sets of reference point pairs, and one set of reference point pairs is used. LLR can be calculated with higher approximation accuracy. In addition, the amount of calculation can be reduced by calculating the LLR using the equation (8) obtained by further approximating the equation (4), which is a simple approximation equation for using two pairs of reference points. Furthermore, the decoding performance of the soft decision error correction decoder can be improved by the LLR calculated with high approximation accuracy.

  As described above, according to the LLR calculator of the first embodiment, an LLR calculator of a receiver that receives a signal that has been transmitted after a bit sequence that has been subjected to error correction coding is modulated by a multi-level modulation scheme. A reference point pair determining unit that selects two reference symbol pairs by selecting two transmission symbol points having a bit subject to LLR calculation of 0 and one of transmission symbol points having a value of 1, a received signal point, and a target bit A square difference calculation unit for calculating a square of a distance between one of the same reference points and a square of a distance between the reception signal point and the other of the reference points having the same target bit; Since the LLR calculation unit that calculates the LLR using the LLR calculation formula provided in advance using the value calculated by the difference calculation unit as a reference, the approximation accuracy of the calculated LLR can be improved.

  Further, according to the LLR calculator of the first embodiment, the LLR calculation unit performs the calculation using the equation (8), so that it is possible to achieve both improvement of the approximation accuracy of the LLR and reduction of the calculation amount. it can.

  Further, according to the LLR calculator of the first embodiment, the reference point pair determination unit determines all or a part of the reference point pairs from the transmission symbol points that are closest to the reception signal point. , LLR approximation accuracy can be improved and the amount of calculation can be reduced.

  Further, according to the LLR calculator of the first embodiment, the transmission symbols that are frequently transmitted in advance or are known to be transmitted are determined as all or part of the reference points. It is possible to improve both the LLR approximation accuracy and reduce the amount of calculation.

Embodiment 2. FIG.
The second embodiment is an example in which the amount of calculation is reduced by further approximating the LLR calculation formula (8) used in the first embodiment.

  Whether 0 is selected for the two max values in Equation (8) or the other term (σ, constant A, a term including the square of the distance) is selected is the distance between the received signal point and the reference point. In addition to the square difference and the value of the constant A, the value of the standard deviation σ of the Gaussian noise is greatly related. When the standard deviation σ is very large, noise is too large and an error that cannot be corrected by the error correction decoder occurs. When the standard deviation σ is very small, the noise is small, and the influence on the error correction capability of the error correction decoder due to the difference in the LLR calculation method is small, so that most errors can be corrected. That is, the magnitude of the standard deviation which is a problem for the communication system is in the middle, and in such a level of standard deviation σ, there is a low possibility that 0 is selected for the two max values in Equation (8). In other words, ignoring the fact that 0 is selected for max in equation (8) and calculating LLR with equation (12) simply replacing max with a non-zero term within max, Approximate degradation is small. Even when the decoding performance evaluation is actually performed in combination with the soft decision error correction decoder, there is no significant difference between Expression (8) and Expression (12).

なお、式（１２）は、２つのｍｉｎそれぞれで選ばれる項がどちらの場合であっても、最下段の式となる。これは２つのｍｉｎが選びうる４通りの場合それぞれに対して式変形を行えば、簡単に確認できる。

Note that Expression (12) is the lowermost expression regardless of which term is selected for each of the two mins. This can be easily confirmed by changing the formula for each of the four cases in which two mins can be selected.

In addition to the deterioration caused by approximating the expression (8), the expression (12) includes the approximate deterioration until the expression (1) is approximated to the expression (8). In some cases, the approximation accuracy is low. There is a possibility. In that case, as in equation (13), correction can be performed by introducing w and B to improve the approximation accuracy. Here, the values of w and B may be searched and determined by computer simulation or the like, and B may be corrected by using only w, with B = 0. Equation (13) becomes Equation (12) if w = 1/2 and B = 0. Here, w and (1-w) correspond to weighting values, and the case where w = 1/2 corresponds to the case where weighting is performed equally. In addition, B corresponds to a correction term that is 0 in some cases, and this indicates that it is not necessary to add B (even if B = 0).

  In the present embodiment, a configuration of an LLR calculator using the lowermost stage of equation (12) and equation (13) for LLR calculation is shown. FIG. 7 is a configuration diagram of the present embodiment. The configuration shown in the figure is the configuration of the LLR calculator 100, which includes two sets of reference point pair determination unit 101, LLR calculation unit 113, and memory 104. That is, the two sets of reference point pair determination units 101 are similar to the two sets of reference point pair determination units 101 of the first embodiment, the transmission symbol point where the bit to be LLR calculation is 0 and the transmission symbol which is 1. Two points are selected and two reference point pairs are determined. In addition, the LLR calculation unit 113 weights and adds two LLRs calculated for each of the two reference point pairs, and a value obtained by adding a correction term that is 0 in some cases to the added value Is calculated as an LLR for the two reference point pairs. As in the first embodiment, the memory 104 is appropriately used to store calculation intermediate values and calculation results generated during the operation of the two sets of reference point pair determination unit 101 and LLR calculation unit 113.

Next, the operation of the LLR calculator of the second embodiment will be described.
Two sets of reference point pair determination units 101 determine two sets of reference point pairs used for LLR calculation. In the second embodiment, the same operation as that of the two reference point pair determining units 101 in the first embodiment is performed. As in the first embodiment, the reference point determined by the two reference point pair determination units 101 may be any transmission symbol point, and this configuration can be realized regardless of the determination method. .

  The LLR calculation unit 113 calculates the LLR based on the equation (12) or the equation (13) using the two reference point pairs determined by the two reference point pair determination units 101. In the calculation, in order to reduce the amount of calculation, the calculation may be performed using an equation obtained by modifying the equation (12) or the equation (13). Further, it may be calculated using a lookup table.

  According to the above configuration, Formula (1), which is an ideal LLR calculation formula, can be approximated by an approximation formula using two sets of reference point pairs, which is higher than using one set of reference point pairs. LLR can be calculated with approximate accuracy. Further, the amount of calculation can be reduced by calculating the LLR using the equation (12) or the equation (13) obtained by further approximating the equation (8) which is the approximate equation of the first embodiment. Furthermore, the decoding performance of the soft decision error correction decoder can be improved by the LLR calculated by the approximate expression with high approximation accuracy using two reference point pairs.

  As described above, according to the LLR calculator of the second embodiment, an LLR calculator of a receiver that receives a signal that is transmitted after a bit string that has been subjected to error correction coding is modulated by a multi-level modulation method. , A reference point pair determination unit that determines two reference point pairs by selecting two transmission symbol points having 0 bits for LLR calculation and two transmission symbol points having a bit of 1, and two reference point pairs Two LLRs calculated for each are weighted and added, and a value obtained by adding a correction term that is 0 in some cases to the added value is calculated as an LLR for two reference point pairs. Since the calculation unit is provided, it is possible to improve both the LLR approximation accuracy and the calculation amount.

  In addition, according to the LLR calculator of the second embodiment, the LLR calculation unit weights the two LLRs equally, so both improvement of the approximation accuracy of the LLR and reduction of the calculation amount are achieved. Can do.

Embodiment 3 FIG.
In the first and second embodiments described above, the LLR is calculated using two reference point pairs. In the third embodiment, a specific method for determining a reference point pair will be described. FIG. 8 shows the configuration of the third embodiment. The configuration of FIG. 8 shows an error correction decoding apparatus in which an LLR calculator 100 and a soft decision error correction decoder 120 are installed. The difference from Embodiments 1 and 2 is that soft decision error correction decoder 120 is configured to feed back an intermediate decoding result to LLR calculator 100.

Hereinafter, the third embodiment will be described in more detail.
The LLR calculator 100 performs the same operation as in the first embodiment and the second embodiment except for how to determine the reference point, and calculates the LLR using the two reference point pairs.
The soft decision error correction decoder 120 performs soft decision decoding using the LLR calculated by the LLR calculator 100 as an input, and outputs an estimated bit string. Also, a decoding intermediate result to be described later is fed back to the LLR calculator 100.

  In the third embodiment, the LLR calculator 100 and the soft decision error correction decoder 120 operate alternately to perform iterative decoding. Since the information fed back from the soft decision error correction decoder is naturally not present when the LLR calculator 100 first receives the received signal, the same operation as in the first and second embodiments is performed. Next, the soft decision error correction decoder 120 feeds back an intermediate decoding result obtained by performing soft decision error correction decoding to the LLR calculator 100. The LLR calculator 100 that has received the decoding intermediate result uses the decoding intermediate result information fed back to the determination of the two reference point pairs, and calculates the LLR by using the two reference point pairs. The above operation is repeated, and when the specified number of times is reached, an estimated bit string is output from the soft decision error correction decoder 120.

  Here, the error correction code implemented in the soft decision error correction decoder 120 may be any error correction code as long as it is a code that can be subjected to soft decision decoding. Examples of such codes include an LDPC code, a turbo code, and a convolution. There are codes, Reed-Solomon codes, and BCH codes. In principle, most of the currently known linear block codes and convolutional codes can be subjected to soft decision decoding.

  The intermediate decoding result fed back by the soft decision error correction decoder 120 may be an intermediate result in the iterative decoding of an LDPC code or a turbo code, or a result of decoding a BCH code or the like. The “intermediate” of the decoding intermediate result is an “intermediate” until the LLR calculator 100 and the soft decision error correction decoder 120 in the present configuration repeatedly operate to reach the specified number of times, and the soft decision error correction decoding. It does not indicate the middle of the operation of the unit 120 alone.

  The information fed back as a result of decoding may be a bit sequence resulting from decoding by the soft decision error correction decoder 120, or may be probability information calculated based on the input LLR. As specific examples of the probability information, an LLR (referred to as a posterior value in this field) obtained as a result of soft decision decoding or an a priori value obtained by subtracting an input LLR from the posterior value can be considered.

  As described above, in the third embodiment, the reference point can be determined by using the decoding result information in which part or all of the bit error is corrected by the soft decision error correction decoder 120, and only the received signal point is determined. Compared with the determination of the reference point, the more important reference point (the reference point close to the bit string transmitted by the transmitter) can be selected and determined. As a result, the approximation accuracy of the calculated LLR can be improved, and the bit error rate of the estimated bits, which is the error correction decoding result finally output from the error correction decoding apparatus of this configuration, can be reduced.

  Next, as an example of the error correction decoding apparatus according to Embodiment 3, the internal configuration of LLR calculator 100 is shown in FIG. The illustrated LLR calculator 100 includes two sets of reference point pair determination units 121, an LLR calculation unit 113, and a memory 104. Further, the soft decision error correction decoder 120 is configured to feed back the intermediate decoding results to the two reference point pair determination units 121. The intermediate decoding result fed back in this configuration is a bit sequence that is a decoding result of the soft decision error correction decoder 120, or when decoding an LDPC code, a turbo code, or the like by iterative calculation, The bit string is calculated when the number of repeated operations reaches a specified number. Of course, a decoding result obtained by performing the iteration operation only once may be used.

Next, the operation of the error correction decoding apparatus shown in FIG. 9 will be described.
The two sets of reference point pair determination units 121 determine one or two pairs of reference points based on the decoding intermediate result fed back from the soft decision error correction decoder 120 (one set was determined based on the feedback) If so, another set is determined by other methods so that a total of two reference point pairs are obtained). For example, the reference point pair determined by the method of Non-Patent Document 1 and the reference point pair determined by the method of Non-Patent Document 2 using feedback are determined as two reference point pairs. In this case, the calculation expression of LLR L _k of the k-th bit in the LLR calculation unit 113 can be expressed as Expression (14) using L _{1, k} and L _{2, k} described in [Background Art]. W and B in Expression (14) are introduced in order to correct approximate deterioration, as in Expression (13). If w = 1/2 and B = 0, the LLR calculation formula in the present embodiment corresponding to the formula (12) is obtained.

  As a matter of course, it is possible to configure an error correction decoding apparatus with two reference point pairs determined by another method. For example, a reference point pair is determined from the vicinity of a transmission symbol point corresponding to a decoding intermediate result. You may choose and decide. Further, assuming that the soft decision error correction decoder 120 feeds back the probability information of each bit as a decoding intermediate result, the transmission probability for each transmission symbol point is calculated based on the probability information, and the transmission symbol point with the highest probability is calculated. The reference points may be selected in order.

  The LLR calculation unit 113 performs the same operation as the LLR calculation unit 113 (FIG. 7) of the second embodiment, but with respect to the two sets of reference point pairs given as an example by the two sets of reference point pair determination units 121. Then, LLR is calculated by the equation (14).

  In the third embodiment, unlike the first and second embodiments, the calculation of the LLR is repeated many times based on feedback. In the course of the repetition, the approximation accuracy can be further improved by changing w and B in Expression (13) and Expression (14) and using different values depending on the number of repetitions. Note that the memory 104 operates in the same manner as in the first and second embodiments.

  According to the above configuration, the reference point can be determined based on the bit string in which part or all of the errors are corrected by the soft decision error correction decoder 120 or the probability information, and only from the received signal point. Compared with determining the reference point, a more important reference point (a reference point close to the bit string transmitted by the transmitter) can be selected and determined. As a result, the approximation accuracy of the calculated LLR can be improved, and the bit error rate of the estimated bits, which is the error correction decoding result finally output from the error correction decoding apparatus of this configuration, can be reduced.

The LLR calculator 100 according to Embodiment 3 is not limited to the configuration shown in FIG. FIG. 10 shows the configuration as an example other than FIG.
The LLR calculator 100 in the configuration of FIG. 10 includes two sets of reference point pair determination units 121, a square difference calculation unit 102 of the distance between a received signal point and a reference point, an LLR calculation unit 103, and a memory 104. The The feedback configuration is the same as in FIG.

The operation of the error correction decoding apparatus shown in FIG. 10 is as follows.
The two sets of reference point pair determination units 121 perform the same operations as the two sets of reference point pair determination units 121 in FIG. Further, the square difference calculation unit 102 between the received signal point and the reference point is the same as the square difference calculation unit 102 (see FIG. 6) of the distance between the received signal point and the reference point in the first embodiment. Perform the operation. Furthermore, the operation of the LLR calculation unit 103 is the same as that of the LLR calculation unit 103 (FIG. 6) in the first embodiment. The memory 104 performs the same operation as in the first embodiment.
The error correction decoding apparatus shown in FIG. 10 can obtain the same effects as the error correction decoding apparatus shown in FIG. Further, by calculating the LLR using the higher approximation accuracy (8), it is possible to calculate the LLR with higher approximation accuracy than the configuration of FIG.

  As described above, according to the error correction decoding apparatus of the third embodiment, the LLR calculator of the first or second embodiment and the soft decision error for performing error correction decoding based on the LLR calculation result from the LLR calculator Since the LLR calculation device includes at least a part of the reference point pair based on the error correction decoding intermediate result in the soft decision error correction decoder, the LLR calculation device reduces the bit error rate of the estimated bits. It can be carried out.

  In addition, according to the error correction decoding apparatus of the third embodiment, since the final decoding result is output from the soft decision error correction decoder after repeating the specified number of times, error correction with a low bit error rate of the estimated bits is performed. The decoding result can be output.

Embodiment 4 FIG.
In the above embodiment, the configuration for calculating the LLR using the two reference point pairs has been described. However, there may be three or more reference point pairs. Such an example will be described below as a third embodiment.

式（１）から式（１５）の導出において、式（１）から削除するｅｘｐの項、つまり、ＬＬＲ算出に用いる３組の基準点ペアはどれでもよく、またどの３組の基準点ペアを選んでも同様の形の式となる。以降の近似も含め、本実施の形態ではＬＬＲ算出に用いる３組の基準点ペアの選び方を限定するものではない。また、３組の基準点ペアを具体的にどう選ぶかについては例を挙げて述べる。First, from the original LLR calculation formula (1) having no approximate deterioration, only the exponential function exp related to the three reference point pairs used for the LLR calculation is deleted, and an approximation formula of Formula (15) is obtained.

In the derivation of the equation (15) from the equation (1), the exp term to be deleted from the equation (1), that is, any of the three reference point pairs used for the LLR calculation, and any of the three reference point pairs Even if you choose, the formula will be similar. In the present embodiment, including the subsequent approximation, the method of selecting the three reference point pairs used for the LLR calculation is not limited. An example of how to select the three reference point pairs will be described.

Equation (15) is further approximated. The expression (16) expresses the exp variable of the expression (15) using x, y, z (x ≧ 0, y ≧ 0, z ≧ 0), and is approximated by the expressions (5) and (6). Is. However, x = min (x, y, z). Further, the same approximation as that performed in Expression (12) of Embodiment 2 was performed, and the determination of max in Expression (6) was approximated assuming that the non-zero term was selected.

Equation (17) is obtained by approximating equation (15) using equation (16). _However, s _j, s l, transmission symbol point and _{s j} closest to the received signal point of _{s h,} similarly s' _j, s' _l, transmission closest to the received signal point of the s' _h a symbol point was s' _j.

Similarly to the second embodiment, the LLR may be calculated using Expression (18) in which correction parameters u, v, and C for approximate deterioration are introduced into Expression (17). Note that C in the equation corresponds to “a correction term that is 0 in some cases”.

  In addition, an LLR calculation formula using four or more reference point pairs can be derived by a similar approximation method. Writing approximate expressions for all of the four or more sets is omitted, but it is possible to derive them by a method within the scope of the above description.

  Next, the LLR calculator 100 in the third embodiment will be described. The LLR calculator 100 according to the third embodiment calculates an LLR using the equations (17) and (18), and its configuration is shown in FIG.

The LLR calculator 100 shown in FIG. 11 includes three sets of reference point pair determination unit 105, LLR calculation unit 133, and memory 104.
The three sets of reference point pair determination unit 105 determine three sets of reference point pairs used for LLR calculation. The three reference point pairs determined here may be any three sets. As an example of the determination method, the combination of the example of the reference point pair determination method described in the embodiments so far corresponds to three sets. The LLR calculating unit 133 calculates the LLR by using the three reference point pairs determined by the three reference point pair determining units 105, using Expression (17) or Expression (18). However, Expression (17) and Expression (18) can be applied only after one reference point closest to the reception signal point is identified among the three reference point pairs. When such a reference point pair is known in advance, the calculation for this determination is not necessary. Further, the memory 104 stores calculation intermediate values and calculation results of the respective units, as in the previous embodiments.

  As described above, in the fourth embodiment, Formula (1), which is an ideal LLR calculation formula, can be approximated by an approximation formula using three sets of reference points, and one or two sets of reference points can be approximated. The LLR can be calculated with higher approximation accuracy than using the pair. Furthermore, the decoding performance of the soft decision error correction decoder can be improved by the LLR calculated with high approximation accuracy.

  As described above, according to the LLR calculator of the fourth embodiment, an LLR calculator of a receiver that receives a signal that is transmitted by modulating a bit sequence that has been subjected to error correction coding by a multi-level modulation method. , A reference point pair determination unit that selects three transmission symbol points having 0 bits for LLR calculation and one transmission symbol point having 1 as a reference point pair, and sets three reference point pairs, respectively. LLR calculation for adding three weighted LLRs calculated with respect to the value, and adding a correction term that is 0 in some cases to the added value as an LLR for three reference point pairs The approximate accuracy of the calculated LLR can be further improved.

  Further, according to the LLR calculator of the fourth embodiment, an LLR calculator of a receiver that receives a signal in which a bit string that has been subjected to error correction coding is modulated by a multi-level modulation scheme and that is transmitted. A reference point pair determining unit that selects four or more transmission symbol points having a bit of 0 and a transmission symbol point of 1 as a plurality of reference point pairs, and a plurality of reference point pairs. Since the calculated LLR is weighted and added, and an LLR calculation unit that calculates a value obtained by adding a correction term that becomes 0 to the added value in some cases as an LLR, the LLR is calculated. The approximation accuracy can be further improved.

Embodiment 5 FIG.
In the third embodiment, two sets of reference points are determined using feedback from the soft decision error correction decoder, but in the fifth embodiment, three reference point pairs are determined using feedback to calculate the LLR. Concerning configuration.

  FIG. 12 is a configuration diagram illustrating the error correction decoding apparatus according to the fifth embodiment. The illustrated error correction decoding apparatus includes an LLR calculator 100, a soft decision error correction decoder 120, and a memory 104. In addition, the LLR calculator 100 includes three sets of reference point pair determination units 115 and LLR operations. The part 133 is installed. The soft decision error correction decoder 120 is configured to feed back the intermediate results of error correction decoding to the three reference point pair determination units 115.

The three sets of reference point pair determination units 115 determine one to three pairs of reference points based on the fed-back decoding result (a total of three reference point pairs are combined with pairs based on other than feedback). decide). For example, the reference point pair determined by the method of Non-Patent Document 1, the reference point pair determined by the method of Non-Patent Document 2 using feedback, and the method of Non-Patent Document 2 using feedback before one iteration. Three reference point pairs are determined from the reference point pairs determined in step (1). In this case, the calculation formula of the LLR _{L k} of k-th bit in the LLR calculation unit 133, _{L 1} described in the background _{art, k} and _{L 2, k,} and _{L 2, k} at the previous repetition L _{'2, k} and Then, the equation (19) is obtained. In this equation (19), u and v in equation (18) are set to u = v = 1/4.

  That is, as shown in the equation (19), the LLR calculation unit 133 sets the LLR for the reference point pair closest to the reception signal point out of the three LLRs calculated for each reference point pair to 2 Add one of the other two LLRs multiplied by one-quarter and add a correction term that is 0 in some cases to the added value to obtain the LLR for three reference point pairs. Calculate as Here, in Equation (19), C corresponds to a correction term that is 0 in some cases.

  Of course, it is also possible to configure three reference point pairs determined by another method. For example, three reference point pairs are selected and determined from the vicinity of the transmission symbol point corresponding to the decoding result. May be.

  The LLR calculation unit 133 performs the same operation as the LLR calculation unit (FIG. 11) of the fourth embodiment. However, Expression (17) and Expression (18) can be applied only after one reference point closest to the reception signal point is identified among the three reference point pairs. However, when such a reference point pair is known in advance, this determination is not necessary. For example, when the three reference point pairs exemplified in the operation of the three reference point pair determination units 115 are determined. This determination is not necessary for, and can be calculated by equation (19). This is because the reference point pair selected for the determination method of Non-Patent Document 1 is closest to the reception signal point.

  Unlike the fourth embodiment, the present embodiment repeats the calculation of the LLR many times based on feedback. In the course of the repetition, the approximation accuracy can be further improved by changing u, w, and C in Expression (17) and Expression (18) and using different values according to the number of repetitions.

  Soft decision error correction decoder 120 performs the same operation as soft decision error correction decoder 120 of the third embodiment. The memory 104 stores calculation intermediate values and calculation results of each unit, as in the previous embodiments.

  Thus, in the fifth embodiment, Formula (1), which is an ideal LLR calculation formula, can be approximated by an approximation formula using three sets of reference points, and one or two sets of reference points can be approximated. The LLR can be calculated with higher approximation accuracy than using the pair. Furthermore, the decoding performance of the soft decision error correction decoder can be improved by the LLR calculated with high approximation accuracy.

  Further, in the fifth embodiment, the reference point can be determined based on the bit string in which part or all of the errors are corrected by the soft decision error correction decoder 120, and the reference point is determined only from the received signal point. Compared to, a more important reference point (a reference point close to a bit string transmitted by a transmitter) can be selected and determined. As a result, the approximation accuracy of the calculated LLR can be improved, and the bit error rate of the estimated bit that is the error correction decoding result that is finally output from this configuration can be reduced.

  As described above, according to the error correction decoding apparatus of the fifth embodiment, the LLR calculation unit is closest to the reception signal point among the three sets of three LLRs calculated for each reference point pair. A value obtained by multiplying the LLR for the reference point pair by 1/2 and the other two LLRs by 1/4 and adding a correction term that is 0 in some cases to the added value is 3 Since the calculation is performed as the LLR for the pair of reference points, the approximation accuracy of the calculated LLR can be further improved.

  In the present invention, within the scope of the invention, any combination of the embodiments, or any modification of any component in each embodiment, or omission of any component in each embodiment is possible. .

  An LLR calculator and an error correction decoding apparatus according to the present invention are an LLR calculator of a receiver that receives a signal obtained by modulating a bit string that has been subjected to error correction coding by a multi-level modulation method, and is an LLR calculation target A reference point pair determination unit that selects two transmission symbol points each having a bit of 0 and a transmission symbol point that is 1 to determine two reference point pairs, and for each of the two reference point pairs An LLR calculation unit that calculates the value obtained by adding the two calculated LLRs in a weighted manner and adding a correction term that is 0 in some cases to the added value as an LLR for two reference point pairs; 2 sets of two reference point pairs are selected by selecting two transmission symbol points whose LLR calculation target bit is 0 and two transmission symbol points being 1, and calculating each of the two reference point pairs. Shi The two LLRs are weighted and added, and the value obtained by adding a correction term that is 0 in some cases to the added value is calculated as the LLR for the two reference point pairs. Therefore, the LLR calculator for calculating the bit LLR representing the reliability of the transmission bit from the symbol coordinates of the reception signal point received by the receiver of the communication system, and the error using the LLR calculator can be improved. The present invention can be applied to a correction decoding apparatus.

  100, 200 LLR calculators, 101, 121 Two sets of reference point pair determination units, 102 A square difference calculation unit (square difference calculation unit) of received signal points and reference points, 103, 113, 133 LLR calculation unit, 104 memory, 105, 115 3 sets of reference point pair determination unit, 110, 120 soft decision error correction decoder, 210 LDPC decoder.

Claims (19)

An LLR calculator of a receiver that receives a signal in which an error correction coded bit string is modulated by a multi-level modulation method and transmitted.
A reference point pair determining unit that selects two transmission symbol points each having a bit that is an LLR (logarithmic likelihood ratio) calculation target and a transmission symbol point that is 1 and determines two reference point pairs;
Two LLRs calculated for each of the two pairs of reference points are weighted and added, and a value obtained by adding a correction term that is 0 in some cases to the added value is used as the two sets of reference points. An LLR calculator comprising: an LLR calculation unit that calculates an LLR for a point pair. The LLR calculator according to claim 1, wherein the LLR calculation unit weights the two LLRs equally. An LLR calculator of a receiver that receives a signal in which an error correction coded bit string is modulated by a multi-level modulation method and transmitted.
A reference point pair determination unit that selects two transmission symbol points each having a LLR calculation bit of 0 and a transmission symbol point of 1 to determine two reference point pairs;
A square difference that calculates the difference between the square of the distance between the received signal point and one of the reference points having the same target bit and the square of the distance between the received signal point and the other of the reference point having the same target bit. A calculation unit;
An LLR calculator, comprising: an LLR calculation unit that calculates an LLR using an LLR calculation formula provided in advance based on a value calculated by the square difference calculation unit. The LLR calculation unit
The received signal point is r, the reference point where the k bit of the two sets of transmission symbols is 0 is s _j , s _l , the reference point where the k bit of the transmission symbol is 1 is s ′ _j , s ′ _l , When the standard deviation of Gaussian noise is σ and the constant term is A,
4. The LLR calculator according to claim 3, wherein LLR calculation of the kth bit is performed using the following equation.

An LLR calculator of a receiver that receives a signal in which an error correction coded bit string is modulated by a multi-level modulation method and transmitted.
A reference point pair determination unit that selects three transmission symbol points whose bit to be LLR calculation is 0 and three transmission symbol points that are 1 to make three reference point pairs;
The three LLRs calculated for each of the three reference point pairs are weighted and added, and a value obtained by adding a correction term that is 0 in some cases to the added value is added to the three sets of reference points. An LLR calculator comprising: an LLR calculation unit that calculates an LLR for a point pair. The LLR calculation unit
For the three LLRs calculated for each reference point pair, multiply the LLR for the reference point pair closest to the received signal point in the three pairs by one-half, and multiply the other two LLRs by one-fourth 6. The LLR calculator according to claim 5, wherein a value obtained by adding a correction term that is zero in some cases to the added value is calculated as an LLR for three reference point pairs. An LLR calculator of a receiver that receives a signal in which an error correction coded bit string is modulated by a multi-level modulation method and transmitted.
A reference point pair determining unit that selects four or more transmission symbol points whose bit to be LLR calculation is 0 and four transmission symbol points that are 1 to make a plurality of reference point pairs;
An LLR calculation unit that calculates, as an LLR, a value obtained by weighting and adding the LLR calculated for each of the plurality of reference point pairs, and adding a correction term that is 0 in some cases to the added value And an LLR calculator. 2. The LLR calculator according to claim 1, wherein the reference point pair determination unit determines all or a part of the reference point pairs from transmission symbol points that are closest to the reception signal point. 4. The LLR calculator according to claim 3, wherein the reference point pair determination unit determines all or a part of the reference point pairs from transmission symbol points that are closest to the reception signal point. 6. The LLR calculator according to claim 5, wherein the reference point pair determination unit determines all or a part of the reference point pairs from transmission symbol points that are closest to the reception signal point. 8. The LLR calculator according to claim 7, wherein the reference point pair determination unit determines all or part of the reference point pairs from transmission symbol points that are closest to the reception signal point. 2. The LLR according to claim 1, wherein the reference point pair determination unit determines, as all or part of the reference points, transmission symbols that are frequently transmitted in advance or are known to be transmitted without fail. Calculator. 4. The LLR according to claim 3, wherein the reference point pair determination unit determines, as all or part of the reference points, transmission symbols that are frequently transmitted in advance or are known to be transmitted without fail. Calculator. 6. The LLR according to claim 5, wherein the reference point pair determination unit determines, as all or part of the reference points, transmission symbols that are frequently transmitted in advance or are known to be transmitted without fail. Calculator. The LLR according to claim 7, wherein the reference point pair determination unit determines transmission symbols that are frequently transmitted in advance or are known to be transmitted as all or part of the reference points. Calculator. An LLR calculator according to claim 1;
A soft decision error correction decoder for performing error correction decoding based on the LLR calculation result from the LLR calculator;
The LLR calculator determines at least a part of a reference point pair based on an error correction decoding intermediate result in the soft decision error correction decoder,
An error correction decoding apparatus characterized by outputting a final decoding result from the soft decision error correction decoder after repeating the series of LLR calculation processing and error correction decoding processing a predetermined number of times. An LLR calculator according to claim 3;
A soft decision error correction decoder for performing error correction decoding based on the LLR calculation result from the LLR calculator;
The LLR calculator determines at least a part of a reference point pair based on an error correction decoding intermediate result in the soft decision error correction decoder,
An error correction decoding apparatus characterized by outputting a final decoding result from the soft decision error correction decoder after repeating the series of LLR calculation processing and error correction decoding processing a predetermined number of times. An LLR calculator according to claim 5;
A soft decision error correction decoder for performing error correction decoding based on the LLR calculation result from the LLR calculator;
The LLR calculator determines at least a part of a reference point pair based on an error correction decoding intermediate result in the soft decision error correction decoder,
An error correction decoding apparatus characterized by outputting a final decoding result from the soft decision error correction decoder after repeating the series of LLR calculation processing and error correction decoding processing a predetermined number of times. An LLR calculator according to claim 7;
A soft decision error correction decoder for performing error correction decoding based on the LLR calculation result from the LLR calculator;
The LLR calculator determines at least a part of a reference point pair based on an error correction decoding intermediate result in the soft decision error correction decoder,
An error correction decoding apparatus characterized by outputting a final decoding result from the soft decision error correction decoder after repeating the series of LLR calculation processing and error correction decoding processing a predetermined number of times.

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